Soft mixer assignment in a hierarchical generative model of natural scene statistics

Odelia Schwartz, Terrence J. Sejnowski, Peter Dayan

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing.

Original languageEnglish (US)
Pages (from-to)2680-2718
Number of pages39
JournalNeural computation
Issue number11
StatePublished - Nov 2006
Externally publishedYes

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience


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